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having trouble solving this

 Sep 28, 2019
 #1
avatar+104962 
+2

 

The graph helps right off :  https://www.desmos.com/calculator/rlynsff8rp

 

 

                       x^2  - 3x                    x ( x - 3)                    1x

f(x) =           ___________  =          ___________  =     _____          (1)

                    2x^2 - 3x - 9                 (2x + 3) (x -3)         2x + 3

 

The "hole"  occurs where x - 3  = 0  →    x  =  3

To find the y coordinate of the "hole"  we have        3                   3         1

                                                                            _______  =      ___  =  __

                                                                             2(3) + 3             9         3

 

So....the "hole" is  at (3, 1/3)

 

The graph shows that the x intercepts and the y intercepts  are the same  ....i.e., at 0

 

The  horizontal  asymptote  is just the ratio of the coefficients  on "x"  in (1)

So.....this is  y  = 1/2

 

The vertical asymptote    is  where 2x + 3  = 0

So

2x + 3 = 0

2x  = -3

x = -3/2

 

 

cool cool cool

 Sep 28, 2019

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